An introduction to the multi-grid method that is used in the majority of finite volume based CFD codes to solve sets of linear algebraic equations.
Time stamps
0:00 Introduction
1:42 Example problem
3:17 Gauss-Seidel iterative solution
5:41 The iteration error
9:04 Spatial error frequencies
12:13 Coarse mesh frequencies
13:48 Aliasing
15:57 Smoothing and solving
18:28 The residual
22:37 Standard Gauss-Seidel algorithm
24:33 The correction equation
28:03 Alternative algorithm
30:37 Summary
31:47 Outro
References
Y. Saad. Iterative Methods for Sparse Linear Systems. 2nd edition. Society
for Industrial and Applied Mathematics, 2003. isbn: 978-0898715347
C. Greenshields, H. Weller 'Notes on Computational Fluid Dynamics: General Principles', Section 5.17. 2022.
doc.cfd.direct/notes/cfd-gene...
============================================
Want to learn more?
============================================
Grab a copy of my CFD Fundamentals Course (for beginners):
www.udemy.com/course/computat...
Learn how to write your own CFD code in MATLAB and python (for intermediates):
dr-aidan-wimshurst-s-school.t...
Learn how I draw my figures and diagrams in Inkscape (for everyone):
dr-aidan-wimshurst-s-school.t...
============================================
Did you like the video?
============================================
Download the lecture slides from my website:
www.fluidmechanics101.com/pag...
Buy me a coffee to say thanks:
www.buymeacoffee.com/NKEZrhvg0
Support the channel on Patreon (and get useful extras for your CFD studies):
/ fluidmechanics101
============================================
Donations:
============================================
1) PayPal
www.paypal.me/fluidmechanics101
==================================
Disclaimer
==================================
The methods, algorithms, equations, formulae, diagrams and explanations in this talk are for educational and demonstrative purposes only. They should never be used to analyse, design, accredit or validate real scientific / engineering / mathematical structures and flow systems. For such applications, appropriate trained, qualified and accredited (SQEP) engineers / scientists should be consulted along with the appropriate documentation, procedures and engineering standards. Furthermore, the information contained within this talk has not been verified, peer reviewed or checked in any way and is likely to contain several errors. It is therefore not appropriate to use this talk itself (or any of the algorithms, equations, formulae, diagrams and explanations contained within this talk) as an academic or technical reference. The reader should consult the original references and follow the verification and validation processes adopted by your company / institution when carrying out engineering calculations and analyses. Fluid Mechanics 101 and Dr. Aidan Wimshurst are not accountable or liable in any form for the use or misuse of the information contained in this talk beyond the specific educational and demonstrative purposes for which it was intended.